• Cut a small corner from the beet packaging and drain off any excess liquid; cut the beets into ½-inch pieces.

In a large bowl, stir together the beets and champagne vinegar. Season with salt and pepper and toss to coat. Let stand, stirring occasionally, while you prepare the rest of the meal.

In a dry large frying pan, place the buns, cut sides down, and cook over medium-high heat until lightly toasted, 1 to 2 minutes. Alternatively, toast them in a toaster oven. Transfer to a plate. Do not clean the pan.

• Peel the onion and cut it crosswise into ½-inch-thick slices; do not separate the rings.

In another large frying pan over medium-high heat, warm 2 to 3 teaspoons oil until hot but not smoking. Add the onion slices, season with salt and pepper, and cook, undisturbed, until golden brown on the bottom side, 4 to 5 minutes. Using tongs or a wide spatula, carefully turn the slices, keeping them intact, and cook until browned on the other side but still slightly crisp, 3 to 4 minutes. Transfer to a cutting board. While the onion is cooking, prepare the burgers.

• Cut a small corner from the burger packaging and drain off any excess liquid. Transfer to a plate; pat dry with a paper towel. Season with salt and pepper. (If using Impossible Burger, with wet hands, form into two [four] ½-inch-thick patties.) 

In the same pan used for the buns, warm 2 to 3 teaspoons oil over medium-high heat until hot but not smoking. Add the patties and cook until starting to brown, 2 to 4 minutes. Turn the patties, top with the cheddar, and cook until the cheddar is melted and the patties are browned, 2 to 4 minutes for medium-rare. Transfer to a plate. Do not clean the pan.

In the same pan used for the burgers, if dry, add 1 to 2 teaspoons butter or oil (from your pantry). Warm over medium heat until hot but not smoking. Crack the eggs directly into the pan and season with salt and pepper. Cook until the whites have set and the yolks are slightly runny, 2 to 3 minutes. If you prefer firmer yolks, cook for 1 to 2 minutes longer. Transfer to a plate. While the eggs are cooking, prepare the salad.

• Trim the root end from the frisée; coarsely chop the frisée.
• Cut away the core from the tomato; thinly slice the tomato. Set aside a few slices for the burgers; coarsely chop the remaining tomato slices for the salad.
• Coarsely chop enough of the cooked onion to measure ¼ cup [½ cup] for the salad; set aside the remaining onion slices for the burgers.

To the bowl with the beets, add the frisée, chopped tomato and onion, and 1 to 2 tablespoons oil and toss to combine. Season to taste with salt and pepper.

Place the bun bottoms and tops, cut sides up, on a work surface and slather both with the pineapple BBQ blend. Top each bun bottom with a burger, tomato slices, a fried egg, and as many onion slices as you like. Close with the bun tops.

Transfer the burgers and beet salad to individual plates and serve.